Let T be an ergodic transformation of a nonatomic probability space, f an L2-function, and K ≥ 1 an integer. It is shown that there is another L2-function g, such that the joint distribution of T i g, 1 ≤ i ≤ K, is nearly normal, and such that the corresponding inner products (Ti f, Tj f) and (T i g, Tj g) are nearly the same for 1 ≤ i, j ≤ K. This result can be used to give a simpler and more transparent proof of an important special case of an earlier theorem , which was a refinement of Bourgain's entropy theorem .
|Original language||English (US)|
|Number of pages||8|
|Journal||New York Journal of Mathematics|
|State||Published - May 21 1998|
- Bourgain's entropy theorem
- Gaussian processes